Introduction to GeoGebra

Tim Brzezinski introduces the webinar on GeoGebra, expressing his passion for creating active, student-centered learning environments. He clarifies that while GeoGebra is his favorite, it's not the only educational tool and encourages educators to explore various apps. Tim provides an overview of the webinar's intent, which is to explore GeoGebra's capabilities and ease of use in the classroom. He also shares his extensive background in math education, having taught high school math and worked at a state university. Tim guides participants to create a GeoGebra account for access to resources and mentions a URL (tinyurl.com/ggbe) for ready-to-use resources.

The presenter delves into GeoGebra's array of applications, emphasizing the nine main apps that are most commonly used. He guides the audience to open GeoGebra Classic, highlighting its versatility and power. Tim showcases the app's various perspectives, including 3D graphics and spreadsheet views. He explains how GeoGebra Classic can display mathematical functions in both 2D and 3D, catering to a wide range of mathematical applications. The segment also touches on the evolution of GeoGebra's apps, how they've been broken down into more specialized tools for easier use, and the presenter's personal recommendation for using the graphing calculator app.

Tim discusses the Graphing Calculator app, noting recent changes that have made it suitable for high-stakes exams by removing certain geometric construction features. He demonstrates the app's functionality, such as graphing expressions, finding intersections, and performing regressions. The presenter also highlights the ease of use and the educational value of these features, comparing GeoGebra's graphing calculator to traditional graphing devices. Additionally, he mentions the app's multilingual support and the ability to adjust settings like decimal places and discusses the app's limitations and upcoming improvements.

The focus shifts to using GeoGebra for data analysis, where Tim demonstrates how to input data points and perform regression analysis. He shows how to use the 'fit line' tool to find the best-fit line for a set of points and discusses the importance of accurate decimal representation in results. The presenter also explains how to manipulate data points and lists within the app, emphasizing the app's capabilities for statistical analysis and its adaptability for various educational needs.

Tim transitions the discussion to the GeoGebra Geometry app, advocating for its use in elementary and middle school education. He praises the app's user-friendly interface and its natural alignment with geometric concepts. The presenter guides the audience through basic operations like plotting points, drawing lines, and creating polygons. He also touches on educational philosophies, emphasizing the importance of student discovery and engagement over traditional teaching methods.

In this segment, Tim explores the Geometry app's capabilities in more depth, showing how to measure angles within polygons and use algebraic views to perform calculations. He demonstrates the app's intuitive nature, allowing for discoveries like the triangle angle sum theorem. The presenter also discusses the app's potential for teaching transformations, such as rotations and dilations, with interactive elements that can enhance students' understanding of geometric principles.

The webinar continues with a demonstration of importing images into GeoGebra and using them for geometric transformations. Tim shows how to import an image, such as Daffy Duck, and apply transformations like rotation and dilation. He discusses the educational value of these features, allowing students to explore geometric concepts in a more visual and interactive manner. The presenter also explains how to adjust the appearance of objects within the app for better clarity and understanding.

Tim further elaborates on the transformations possible within the Geometry app, with a focus on dilation. He demonstrates how to dilate objects around a point and discusses the mathematical concepts that emerge, such as the effects of different scale factors. The presenter encourages the use of these tools to facilitate student discovery and understanding of geometric principles, such as parallel lines and proportional relationships.

The presenter discusses the process of saving and sharing GeoGebra constructions, guiding users on how to save their work and access it later. He explains the difference between viewing and editing modes and how to make copies of constructions for further editing. Tim also touches on the organization of saved files within the user's GeoGebra profile and the ease of accessing them for future use.

Tim introduces the 3D Calculator app, showcasing its potential on both web and mobile platforms. He demonstrates the app's capabilities, such as plotting points in 3D space and creating 3D shapes like cubes. The presenter emphasizes the app's educational value in fostering spatial reasoning skills, which he believes are often neglected in traditional math education. He also encourages teachers to explore the app's features to enhance their students' understanding of three-dimensional geometry.

The focus of this segment is on creating 3D models and surfaces using GeoGebra's 3D Calculator app. Tim demonstrates how to create a cone through a simple function and then shows how to transform it into a surface of revolution. He encourages teachers to explore these features with their students to enhance their understanding of 3D geometry and calculus concepts. The presenter also highlights the app's augmented reality feature, which allows students to visualize 3D models in their environment, further enhancing the learning experience.

In the final segment, Tim announces an upcoming webinar and invites participants to join. He reflects on the webinar's content, emphasizing the potential of GeoGebra to transform math education. The presenter expresses his enthusiasm for the app's capabilities and encourages teachers to continue exploring GeoGebra with their students. He also invites questions from the audience and offers to stay back to address any queries.